Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Title: Understanding the Difference of Squares**
**Concept Example:**
Expression: \( x^2 - 64 \)
**Explanation:**
- The expression \( x^2 - 64 \) is a classic example of a mathematical concept known as the "difference of squares."
- The difference of squares formula is expressed as:
\[
a^2 - b^2 = (a + b)(a - b)
\]
In this case, \( a = x \) and \( b = 8 \) (since \( 64 = 8^2 \)), so the expression can be factored as:
\[
x^2 - 64 = (x + 8)(x - 8)
\]
- Understanding and applying the difference of squares helps simplify expressions and solve equations efficiently.
**Importance in Mathematics:**
The difference of squares is a foundational algebraic identity used in simplifying expressions, solving quadratic equations, and integral calculus. Mastery of this concept provides a deeper understanding of polynomial identities and their applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2Fb707e4b1-f056-4aae-98e5-64286f15b63d%2Fenx8jqf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding the Difference of Squares**
**Concept Example:**
Expression: \( x^2 - 64 \)
**Explanation:**
- The expression \( x^2 - 64 \) is a classic example of a mathematical concept known as the "difference of squares."
- The difference of squares formula is expressed as:
\[
a^2 - b^2 = (a + b)(a - b)
\]
In this case, \( a = x \) and \( b = 8 \) (since \( 64 = 8^2 \)), so the expression can be factored as:
\[
x^2 - 64 = (x + 8)(x - 8)
\]
- Understanding and applying the difference of squares helps simplify expressions and solve equations efficiently.
**Importance in Mathematics:**
The difference of squares is a foundational algebraic identity used in simplifying expressions, solving quadratic equations, and integral calculus. Mastery of this concept provides a deeper understanding of polynomial identities and their applications.
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